Distributionally robust joint power and admission control via SOCP deflation

Joint power and admission control (JPAC) aims at supporting a maximum number of links at their specified signal to interference plus noise ratio (SINR) targets while using a minimum total transmission power. Almost all of the existing works on JPAC assume perfect channel state information (CSI). However, this assumption generally does not hold true. In this work, we consider the chance (probabilistic) SINR constrained JPAC problem, where each link's SINR outage probability is enforced to be less than or equal to a given tolerance. In this paper, we handle the computationally intractable chance SINR constraints by doing sample approximations. The sample approximation scheme not only simplifies the difficult chance SINR constraint into finitely many (depending on the sample size) simple linear constraints, but also relaxes the assumption of channel distribution information (CDI), thus being distributionally robust. Furthermore, we reformulate the sample approximation problem as a group sparse minimization problem and then relax it to a second-order cone program (SOCP). The solution of the SOCP relaxation problem can be used to check the simultaneous supportability of all links in the network and to guide an iterative link removal procedure (deflation). We illustrate the effectiveness of the proposed distributionally robust sample approximation-based SOCP deflation approach by using a nonrobust counterpart as the benchmark.